1. Field of the Invention
This invention concerns those accelerometers in which an acceleration measurement is deduced from a measurement of the forces required to hold a test weight still or bring it back to a position defined with respect to a body of the apparatus. The invention concerns more particularly those accelerometers wherein these forces are electrostatically produced.
In this case, a force generator employs a series of n electrodes E.sub.1, E.sub.2, . . . E.sub.i, . . . , E.sub.n set out around the test weight and integral with the body of the accelerometer. The parameters are denoted as follows:
V.sub.0 : potential of the test weight, PA1 v.sub.i : potential of the electrode E.sub.i, PA1 C.sub.i : capacity of the electrode E.sub.i with respect to the test weight, PA1 x, y, z: coordinates of the center of the test weight within a reference frame x, y, z, associated with the body of the accelerometer, PA1 .theta., .PSI., .PHI.: three angles defining the attitude of the test weight with respect to the reference frame x, y, z.
For small angles .theta., .PSI. and .PHI. correspond to rotations respectively about the axes x, y and z. ##EQU1## gradient operator in relation to the variables x, y, z; ##EQU2## gradient operator in relation to the variables .theta., .PSI., .PHI..
If applied to the capacities C.sub.i, these gradient operators give rise to the following in the reference frame x, y, z: ##EQU3##
Using these notations, it can be shown that the electrostatic force F and couple exerted on the test weight may be expressed as follows in the reference frame x, y, z: ##EQU4##
Only the value of the electrostatic force F has any bearing in how the accelerometer works, but to determine said force, in addition to the measurements of the potentials V.sub.i, the values must be known of the gradients ##EQU5## and potential V.sub.0 of the test weight.
2. Description of the Prior Art
The method of determining the gradient ##EQU6## on the one hand and zero cueing of the potential V.sub.0 on the other hand has already been discussed in U.S. Pat. No. 4,393,710 issued July 19, 1983.
Accelerometers of the electrostatic type are already known through U.S. Pat. No. 3,742,767 issued July 3, 1973 and French Pat. No. FR-A-2511509 filed Dec. 31, 1980.
The accelerometer disclosed in the former patent is an ultrasensitive accelerometer using a spherical conductive ball floating in a spherical hollow cage as a test weight. The latter patent discloses a navigation accelerometer.
DE-B-1137241 filed Apr. 13, 1961 discloses an accelerometer having a cubic or spherical test weight, a pressure sensing or capacitive position detection system and a pressurized air position control system. With a view to developing an ultra-sensitive accelerometer, the electrostatic suspension of a spherical weight offers the advantage of requiring position slaving in three axes only (rotations are left free). Along each axis, differential capacitive measurements made by means of diametrically opposed electrodes (E.sub.1 and E.sub.2 in FIG. 1) determine the translation of the sphere and hence the acceleration to which the center of mass G thereof is subjected.
The use of spherical test weights has a further advantage. There is no need to provide the surface of a sphere with metal portions delimited from one another and forming one of the armatures of the position detection and position control capacitors. Those armatures are nothing other than those parts of the conducting ball which are opposite the armatures on the inner cage wall.
In the case of an ideal weight, shaped perfectly as a spheroid and having equal potential, the mechanical and electrical properties are isomorphic for any change of a reference frame centered at the cage center. Any rotation would therefore leave the capacities unchanged and likewise the potential differences between the electrodes and the test weight.
In practice, shortcomings in sphericity and fluctuations in potential of the test weight can adversely affect performance of the accelerometer when the surface parts of the floating weight, positioned opposite the electrodes, change with rotation.
Thus, by way of an example:
(a) rotation .phi. of the test weight (FIG. 1) about the axis z is likely to cause a variation in the difference C.sub.2 -C.sub.1 of the capacities in the absence of any change in position of the center of mass G of the sphere. Under these conditions, slaving in translation along the axis x recenters the test weight in such a way as to restore equality in the capacities C.sub.1 and C.sub.2. The acceleration imparted to the test weight for this recentering operation has a direct adverse effect on the measurement by producing low frequency noise (n times the frequency of rotation of the sphere for a sphericity defect of order n);
(b) if the slaving pass band is sufficiently large to ensure equality in the capacities C.sub.1 and C.sub.2 with negligible error, the simultaneous variations in these capacities correspond essentially to variation .DELTA.e in the mean distance e between the electrodes and the sphere. As far as the accelerometer is concerned, this results in a relative sensitivity variation equal to ##EQU7## Hence, for an ultra-sensitive accelerometer such as that discussed above (intended to measure solely accelerations less than 10.sup.-4 m/s.sup.2), the following values are obtained for a test weight 4 cm in diameter associated with 25 mm.sup.2 electrodes: EQU e.congruent.300 .mu.m EQU .DELTA.e.gtoreq.0.1 .mu.m ##EQU8##
For less sensitive accelerometers, the situation is worse since the dimension e must be reduced to obtain the necessary electrostatic forces with applied voltages of reasonable proportions (&lt;300 volts);
(c) despite the care taken in fabricating the spherical test weight and the choice of conducting materials from which it is formed, the fluctuations in potential experienced at the surface of this sphere can reach several tens of millivolts. When the sphere turns, these fluctuations in potential are at the root of variations in the interactive electrostatic forces between the test weight and the conductors arranged thereabout (electrodes and cage).
A further difficulty experienced with a floating spherical test weight stems from variations in the geometry of the spaces between the electrodes and the sphere when the latter moves orthogonally to the sensitive axis that is theoretically the axis of the electrodes.
These variations in geometry give rise to non-linear coupling between the accelerometer axes: the application of voltages to the electrodes used for translationally slaving the sphere along the axis y (FIG. 2a) causes a parasite force along the axis x when the sphere is decentered under the effect of, for instance, an acceleration along x (FIG. 2b), even if the axes x and y are perfectly perpendicular. In the case of ultra-sensitive accelerometers, designed for spatial applications, the coefficients of sensitivity cannot be determined on the ground where such accelerometers are saturated by the acceleration due to gravity. It then becomes very difficult to determine and take account of these coupling effects.
All the sources of error educed above are particularly detrimental when the accelerators are intended for measuring the gradients of gravity, that is, accelerometers having ultra high sensitivity and accuracy as good as that required for navigation accelerometers.
In particular, linear accelerometers should be designed with very faithful sensitivity for carrying out differential measurement between accelerometers (measurement of gravity gradients in spatial orbit).